Journal ArticleDOI
Indentation size effects in crystalline materials: A law for strain gradient plasticity
William D. Nix,Huajian Gao +1 more
TLDR
In this article, the indentation size effect for crystalline materials can be accurately modeled using the concept of geometrically necessary dislocations, which leads to the following characteristic form for the depth dependence of the hardness: H H 0 1+ h ∗ h where H is the hardness for a given depth of indentation, h, H 0 is a characteristic length that depends on the shape of the indenter, the shear modulus and H 0.Abstract:
We show that the indentation size effect for crystalline materials can be accurately modeled using the concept of geometrically necessary dislocations. The model leads to the following characteristic form for the depth dependence of the hardness: H H 0 1+ h ∗ h where H is the hardness for a given depth of indentation, h, H0 is the hardness in the limit of infinite depth and h ∗ is a characteristic length that depends on the shape of the indenter, the shear modulus and H0. Indentation experiments on annealed (111) copper single crystals and cold worked polycrystalline copper show that this relation is well-obeyed. We also show that this relation describes the indentation size effect observed for single crystals of silver. We use this model to derive the following law for strain gradient plasticity: ( σ σ 0 ) 2 = 1 + l χ , where σ is the effective flow stress in the presence of a gradient, σ0 is the flow stress in the absence of a gradient, χ is the effective strain gradient and l a characteristic material length scale, which is, in turn, related to the flow stress of the material in the absence of a strain gradient, l ≈ b( μ σ 0 ) 2 . For materials characterized by the power law σ 0 = σ ref e 1 n , the above law can be recast in a form with a strain-independent material length scale l. ( builtσ σ ref ) 2 = e 2 n + l χ l = b( μ σ ref ) 2 = l ( σ 0 σ ref ) 2 . This law resembles the phenomenological law developed by Fleck and Hutchinson, with their phenomenological length scale interpreted in terms of measurable material parametersbl].read more
Citations
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Journal ArticleDOI
A conventional theory of mechanism-based strain gradient plasticity
TL;DR: In this article, a conventional theory of mechanism-based strain gradient plasticity is established, and the difference between this theory and the higher-order MSG plasticity theory based on the same dislocation model is only significant within a thin boundary layer of the solid.
Journal ArticleDOI
Experimental characterization of shear transformation zones for plastic flow of bulk metallic glasses
TL;DR: Experimental characterization of shear transformation zones (STZs) for plastic flow of bulk metallic glasses (BMGs) based on a newly developed cooperative shearing model provides compelling evidence that the plastic Flow of metallic glasses occurs through Cooperative shearing of unstable STZs activated by shear stresses.
Journal ArticleDOI
Update on a class of gradient theories
TL;DR: In this paper, the authors provide an update of the standard theories of dislocation dynamics, plasticity and elasticity properly modified to include scale effects through the introduction of higher order spatial gradients of constitutive variables in the governing equations of material description.
Journal ArticleDOI
A unified treatment of strain gradient plasticity
TL;DR: In this article, a theoretical framework is presented that has potential to cover a large range of strain gradient plasticity effects in isotropic materials, including both incremental plasticity and viscoplasticity.
Journal ArticleDOI
A further step towards an understanding of size-dependent crystal plasticity: In situ tension experiments of miniaturized single-crystal copper samples
TL;DR: In this article, the size effects of the plastic deformation behavior of copper single crystals loaded along the 〈−2.3.4'' direction were investigated and a method for in situ testing of miniaturized tension specimen was developed.
References
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Journal ArticleDOI
The deformation of plastically non-homogeneous materials
TL;DR: The geometrically necessary dislocations as discussed by the authors were introduced to distinguish them from the statistically storages in pure crystals during straining and are responsible for the normal 3-stage hardening.
Journal ArticleDOI
Strain gradient plasticity: Theory and experiment
TL;DR: In this paper, a deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening, which is a non-linear generalization of Cosserat couple stress theory.
Journal ArticleDOI
A phenomenological theory for strain gradient effects in plasticity
TL;DR: In this paper, a strain gradient theory of plasticity is introduced, based on the notion of statistically stored and geometrically necessary dislocations, which fits within the general framework of couple stress theory and involves a single material length scale l.
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An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments
Warren C. Oliver,George M. Pharr +1 more